As in description, various laser designator beams should be visible in NV/IR optics.
Most such devices use near infrared wavelength of 1.064 micrometers (1064 nanometers), produced by Nd:YAG solid state laser (see references). This wavelength is well visible with regular cameras with weak IR filters and with NV/IR equipment.
SOFLAM beams are well visible through NV - and, at the moment, so is the terminal point; hence, the beam should be visible as well.
Same applies for helicopter lasers used to guide missiles. See attached videos.